The fast for the curious

Classical Mechanics Level 4

We define x = ( t 2 − t 1 ) / 2 x=(t_2-t_1)/2 as the distance between Finn and Aaron. It should not depend on the time when Finn sends the light pulse. For all the other definitions if Finn sent the light pulse later the distance would increase.

What is the numerical value of the speed of light if we define distances and times as in the previous problem/set?

186,282.3971 0 1 3 × 1 0 8 3 \times 10^8

David Mattingly by David Mattingly

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1 solution

Siam Habib
Jun 25, 2014

Notice that d = v × Δ t d = v \times \Delta t where d d is the distance, v v is the velocity of some object and Δ t \Delta t is the time it requires to travel it.

In the previous question if the distance between Finn and Aaron was d d then light traveled 2 d 2d distance on an time interval of t 2 − t 1 t_2 -t_1 . So, if c c is the velocity of light then in the former system d = t 2 − t 1 2 = t 2 − t 1 2 × c ⇒ c = 1 d = \frac{t_2-t_1}{2} = \frac{t_2-t_1}{2} \times c \Rightarrow c = 1 .

So, the numerical value of the velocity of light in the system described in the former question was 1 1 .

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